{"paper":{"title":"Sch\\\"utzenberger Products in a Category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Henning Urbat, Liang-Ting Chen","submitted_at":"2016-05-06T03:31:11Z","abstract_excerpt":"The Sch\\\"utzenberger product of monoids is a key tool for the algebraic treatment of language concatenation. In this paper we generalize the Sch\\\"utzenberger product to the level of monoids in an algebraic category $\\mathscr{D}$, leading to a uniform view of the corresponding constructions for monoids (Sch\\\"utzenberger), ordered monoids (Pin), idempotent semirings (Kl\\'ima and Pol\\'ak) and algebras over a field (Reutenauer). In addition, assuming that $\\mathscr{D}$ is part of a Stone-type duality, we derive a characterization of the languages recognized by Sch\\\"utzenberger products."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01810","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}